Quadratic Roots & Solving Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, express it in the form (px + q)(rx + s) = 0, where p, q, r, and s are constants that satisfy the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the roots of the equation 12x = 9x² + 4?

Back

Rearrange to 9x² - 12x + 4 = 0, then factor to (3x - 2)(3x - 2) = 0, giving roots x = 2/3.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions to the equation 7(x-10)(3x+2) = 0?

Back

Set each factor to zero: x - 10 = 0 (x = 10) and 3x + 2 = 0 (x = -2/3). Solutions are x = 10 and x = -2/3.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a function to have zeros?

Back

Zeros of a function are the x-values where the function's output is zero, indicating the points where the graph intersects the x-axis.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the zeros from a graph?

Back

Identify the x-coordinates of the points where the graph intersects the x-axis.

Front

What is an ordered pair in the context of quadratic roots?

Back

An ordered pair (x, 0) represents the x-coordinate of the root of the quadratic equation, indicating where the graph crosses the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.